I'm bundling gear rewards with experience point rewards here, because better gear ultimately ends up in you being able to earn xp faster in the future, so it is just a more indirect method of getting you experience point rewards. And of course all this is only true below the level cap, we all know how much for example WoW changes at level 60.
So if you look at the reward for solo play, it is relatively easy. You log on, you play, and you get rewards which are more or less linear with the time you spent during the play session. So
Solo session reward = Solo session time x Solo reward ratewith the solo reward rate being the rate at which you earn rewards like xp and gear during a typical solo session, from killing mobs alone, and from quests.
The reward for group play is slightly more difficult. After you log on, you first need some time to actually find a group, and to gather at the same spot. During that group finding time your rewards earned are zero. Only then does reward earning start, thus
Group session reward = (Group session time - Group finding time) x Group reward rate
So if people are trying to maximize the reward per session, they would prefer soloing if the solo session reward is bigger than the group session reward. But they would prefer to group if the group session reward is bigger than the solo session reward. As the term of the group finding time is always greater than zero, if the solo reward rate is equal than the group reward rate, the group session reward is diminished by the group finding time term, and people prefer soloing, because it gives greater rewards.
So what can developers do to persuade people to group? Well, the devs are in control of many of the parameters in these equations, especially the reward rates. One crude, but working approach, taken by the original Everquest, was to diminish the solo reward rate from a certain level on to be zero or near zero. Some classes were simply totally unable to gain any experience points while solo, as the lowest level of mobs still giving xp was too tough to kill. Obviously players resent that sort of "forced grouping".
So a subtler approach is to make the group reward rate slightly bigger than the solo reward rate, so as to encourage grouping, without making soloing impossible. This is something Blizzard definitely at least tried in World of Warcraft. The xp per hour rewards are difficult to compare, but it is very clear that the item rewards from group play are better than the item rewards from solo play. The reason why WoW failed to balance these two better, is in the time terms, which are harder to control. If it takes half an hour to find and gather a group, that is not much if the group stays together for 3 or more hours. But if they stay together for only 1 hour or so, the negative effect of the group finding time on the reward becomes too significant. In World of Warcraft it seems that the average player plays in relatively short sessions (the famous "casual" player), the group reward rate isn't so much bigger than the solo reward rate to balance out the rewards lost during the waiting time, and so many people just go soloing. Changing the reward rates in a patch would be difficult. You can't diminish solo rewards without causing a huge outcry of "nerf!". Increasing the group rewards is possible, for example when Everquest wanted more people to visit dungeons, they simply added a dungeon xp bonus to the game.
But even more effective would be for the developers to introduce tools that diminish the group finding time. World of Warcraft could make huge improvements in their looking for group tools. And meeting stones could be reprogrammed to work like a warlock summoning, so the first three people arriving at the dungeon could summon the two stragglers. The beauty of such changes would be that at first sight they don't change the rewards rate at all. But by cutting down on the rewards lost to a group due to waiting, improved group finding and gathering tools would make grouping relatively more attractive to players, and lead to more positive social interaction between them. We are not a bunch of hermits preferring to play alone, it is the parameters of the game that influence our behavior and preference for soloing or grouping.
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